FIAT LUX ACADEME
CAVITE
Columnar Lesson Plan in General Mathematics
Week 1 – September 11 – 15, 2023
Subject Matter
Topic:
Functions and Their
Graphs
 Functions
 Evaluating Functions
 Piecewise-Defined
Functions
 Operation on Functions
References:
Books
Benjamin, J. B., &
Oryan, S. (2017).
Mathematics Skills for
life. Abiva Publishing
House, Inc.
Escaner , J. M. (2017).
Math Digest Genaral
Mathematics. Trinitas
Publishing, Inc.
Gabuyo, Y., &
Cristobal, R. (2019).
21st Century Skills
General Mathematics.
Objectives
Activities
Day 1
September 11, 2023 (Monday):
G11 TVL Bacon (7:00 A.M. - 9:00 A.M.)
G11 TVL Bacon (10:30 A.M. - 11:30 A.M.)
G11 STEM Curie (8:00 A.M. - 10:00 A.M.)
G11 STEM Darwin (3:10 P.M. - 5:10 P.M.)
September 12, 2023 (Tuesday):
G11 STEM Raffiñan (8:00 A.M. - 10:00 A.M.)
G11 STEM Einstein (10:30 A.M. -12:30 A.M.)
G11 STEM Del Mundo (3:10 P.M. - 4:10 P.M.)
September 14, 2023 (Thursday):
G11 STEM Del Mundo (3:10 P.M. - 4:10 P.M.)
Day 2
September 13, 2023 (Wednesday):
G11 TVL Bacon (7:00 A.M. - 9:00 A.M.)
G11 TVL Bacon (10:30 A.M. - 11:30 A.M.)
G11 STEM Curie (8:00 A.M. -10:00 A.M.)
G11 STEM Darwin (3:10 A.M. - 4:10 A.M.)
September 14, 2023 (Thursday):
G11 STEM Raffiñan (8:00 A.M. -10:00 A.M.)
G11 STEM Einstein (10:30 A.M. -12:30 P.M.)
G11 STEM Del Mundo (4:10 P.M. -5:10 P.M.)
September 15, 2023 (Friday):
G11 STEM Del Mundo (8:00 A.M. -9:00 A.M.)
G11 STEM Darwin (9:00 A.M. -10:00 A.M.)
Evaluation/Assessment
Remarks
The Inteligente
Publishing, Inc.
Isidro, J. D., Solano, I.
P., & Mariano, O. G.
(2019). General
Mathematics (Second).
Diwa Learning
Systems Inc.
Digital Sources
Estela,
M.
(2022,
August 14). Vertical
Line Test. ChiliMath.
https://www.chilimath.
com/lessons/intermedia
te-algebra/vertical-linetest/
Materials:
Laptop
PowerPoint Presentation
LCD TV
WhiteBoard
•
evaluate a
function
Motivation:
“Function Machine”
The class will be divided into six (6) groups. Each
group will be given materials need in this activity
Online meeting: break out rooms, Microsoft
whiteboard app
Onsite meeting: Manila paper, and marker
Mechanics
1. I’ll be presenting a function machine and a set
of input to be process in the machine
2. Every member will collaborate or brainstorm
to find the output in the given machine. The
first group to write and raise the correct output
will gain 2 points
3. The group that will have the highest score will
be the winner.
“double x
then adds 5”
Questions:
1. If 7 goes into the machine, what number comes
out?
2 (7) + 5 = 19
2. If 13 goes into the machine, what number comes
out?
2 (13) + 5 = 31
3. If -5 goes into the machine, what number comes
out?
2 (-5) + 5 = -5
*Students will be
collaborating with their
classmate from this
activity. They will be
task to complete each
equation in order to find
the output based on the
given.
4. If x goes into the machine, what comes out?
2 (x) + 5 = 2x + 5
5. If 3x goes into the machine, what comes out?
2 (3x) + 5 = 6x + 5
Vocabulary Development:
Relation
Domain
Range
Function
Vertical Line Test
Piecewise Function
Focused Discussion:

Recall discussion about
exemplifying examples
Relation
and
Def. 1 Let A and B be any two empty nonempty sets.
Then the cross product of A and B, denoted by A x B is
given by
𝐴 × 𝐵 = {(𝑎, 𝑏)} 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑎 ∈ 𝐴 𝑎𝑛𝑑 𝑏 ∈ 𝐵}
This means that A x B is a set of ordered pairs and this
establishes a relation or an association between
elements of the first set A and the second set B
Example:
R = {(1,2), (2,3), (5,4), (5,5), (5,7)}
In the figure , a relation between sets X and Y can be
established. The relation is indicated by the arrows.

Illustrating a Function and explaining how to
categorize a relation as a function
Def. 1 A functions from set A to setB is a set of
ordered pairs (or is a relation) such that each element
in A is associated to a unique element in B. That is,
two ordered pairs have the same first element
Note: All functions are relations, however, not all
relations are functions.
Example:
(a) This is a function
(b) This is a function
(c) This is NOT a function


identify the
methods to
determine if a
given relation
represent
function.
Enumerating the ways on how to identify
a function
Functions can be represented in different ways
1. Ordered Pairs
{(1,2), (2,3), (5,4), (5,5), (5,7)}
2. Mapping or arrow diagram
3.
Equation
y = 2x + 5
Note: if an element of domain corresponds to two
range, then it’s not a function.
Let’s Try this!
1. Which of the following are functions?
e ={(3,2), (4,0), (5,1), (2,3)}
l = {(3,2), (3,4), (3,1), (3,3)}
f = {(1,3), (2,6), (3,9),… (n,3n),…}
*Students will analyze
the given and will
identify the function in
the given relation,
students will also justify
their answers
2. Determine whether the relationship given in the
mapping diagram is a function.
3. Determine whether the relationship given in the
mapping diagram is a function.

Explain what is a vertical line test and
show examples of it.
Vertical Line Test
 method that is used to determine whether a
given relation is a function or not.
 If a vertical line intersects the graph of a
relation at exactly one point, it implies that a
single x-value is only paired to a unique value
of y. then the relation is a function.
 If a vertical line intersects the graph in some
places more than once, then the relation is NOT
a function.
*Answering questions
Example:
(a) This is a function
(b) This is NOT a function
Let’s Try this!
1. Which of the following can be the graph of a
function?
*Students will analyze
the graphs shown and
will justify their answers
2. Which of the following can be the graph of a
function?
3. Which of the following can be the graph of a
function?

Identifying which of the
equations shows a function
following
Which of the following equations describe a function?
o 𝑦 = 2𝑥 + 1
o 𝑥2 + 𝑦2 = 1
o 𝑥2 + 𝑦 = 0
o 𝑦 = 𝑥 2 − 2𝑥 + 2
*Students will examine
the said equation and
will be instructed to
install the “Desmos”
application which helps
to graph an equation.
o 𝑦 = √𝑥 + 1
o 𝑦=
2𝑥+1
𝑥−1
Note: Explanation and follow up questions are
included after identifying the equations that describe a
function.


Discuss the Piecewise function and show
an illustration and examples.
Piecewise Function
illustrating
 A function defined by sub functions, where
piecewise
each sub functions applies to a certain interval
functions to
of the main function’s domain
facilitate
understanding and Example:
Imagine a function
application
2



when x is less than 2, it gives x
when x is exactly it gives 6
when x is more than 2 and less than or equal to
6 it gives the line 10 - x
It is look like this
And we write it like this:
Another example:
Graph:
Follow up questions:
What is h(−1)?
x is ≤ 1, so we use h(x) = 2, so h(−1) = 2
What is h(1)?
x is ≤ 1, so we use h(x) = 2, so h(1) = 2
What is h(4)?
x is > 1, so we use h(x) = x, so h(4) = 4
*Recitation
*Students will answer
Let’s Try This!
 A cell phone company uses the function below to this on their paper
determine the cost, C, in pesos for g gigabytes of
data transfer.
*Board work
Find the cost of using 1.5 gigabytes of data and
the cost of using 4 gigabytes of data.

Illustrate the Law of Substitution
If a + x = b and x = c, then a + c = b
Given 𝑓(𝑥) = 3𝑥 − 2, find:
1. 𝒇(𝟑)
𝑓(3) = 3𝑥 − 2
𝑓(3) = 3(3) − 2
𝑓(3) = 9 − 2
𝑓(3) = 𝟕
2. 𝑓(−2)
𝑓(−2) = 3𝑥 − 2
𝑓(−2) = 3(−2) − 2
𝑓(−2) = −6 − 2
𝑓(−2) = −𝟖
Given𝑔(𝑖) = 𝑖 2 − 4𝑖 + 9, find g (-3)
𝑔(−3) = (−3)2 − 4(−3) + 9
𝑔(−3) = 9 + 12 + 9
𝑔(−3) = 𝟑𝟎
*Students will answer
the given in a sheet of
paper.
*Students will answer
this on their paper.

•
represent real-life
situations using
function,
including
piecewise
function
Enumerate the Operation of Functions
Operation of Functions
Let f and g be any two functions.
The sum 𝑓 + 𝑔, difference 𝑓 − 𝑔, product 𝑓𝑔,and
𝑓
quotient 𝑔 are functions whose domains are the set
of all real numbers common to the domain of f and
g, and defined as follows:
Let f and g be any two functions.
(a) Their sum, denoted by f + g , is defined by
(𝒇 + 𝒈)(𝒙) = 𝒇(𝒙) + 𝒈(𝒙)
Example:
Let 𝑓(𝑥) = 2𝑥 + 1 and 𝑔(𝑥) = 𝑥 2 − 4
= 𝑓(𝑥) + 𝑔(𝑥)
= (2𝑥 + 1) + (𝑥 2 − 4)
= 𝒙𝟐 + 𝟐𝒙 − 𝟑
*Students will be asked
about the steps in solving
the sum of a function
Let f and g be any two functions.
(b) Their difference, denoted by f - g , is defined
by
(𝒇 − 𝒈)(𝒙) = 𝒇(𝒙) − 𝒈(𝒙)
Example:
Let 𝑓(𝑥) = 2𝑥 + 1 and 𝑔(𝑥) = 𝑥 2 − 4
= 𝑓(𝑥) − 𝑔(𝑥)
= (2𝑥 + 1) − (𝑥 2 − 4)
*Answering questions
about the steps in solving
the difference of a
function
= −𝒙𝟐 + 𝟐𝒙 + 𝟓
Let f and g be any two functions.
(c) Their product, denoted by 𝑓 ⋅ 𝑔 , is defined by
(𝒇𝒈)(𝒙) = 𝒇(𝒙) ⋅ 𝒈(𝒙)
Example:
Let 𝑓(𝑥) = 2𝑥 + 1 and 𝑔(𝑥) = 𝑥 2 − 4
= 𝑓(𝑥) ⋅ 𝑔(𝑥)
= (2𝑥 + 1)(𝑥 2 − 4) → FOIL method
= 𝟐𝒙𝟑 + 𝒙𝟐 − 𝟖𝒙 − 𝟒
*Students will be asked
regarding the operation
and what technique will
be used
Let f and g be any two functions.
(d) Their quotient, denoted by
𝑓
𝑔
, is defined
by
𝒇
𝒇(𝒙)
( ) (𝒙) =
𝒈
𝒈(𝒙)
Example:
2
Let 𝑓(𝑥) = 2𝑥 + 1 and 𝑔(𝑥) = 𝑥 − 4
𝑓(𝑥)
=
𝑔(𝑥)
𝟐𝒙 + 𝟏
= 𝟐
, 𝒙 ≠ ±𝟐
𝒙 −𝟒
•
perform addition,
subtraction,
multiplication,
division and
composition of
functions
Let’s Try This
Evaluate the following using the operation of
functions: sum, difference, product and quotient.
1. f(x) = 2x + 3 and g(x) = x2
2. f(x) = 2x2 + 2 and g(x) = 6x
*Students are asked the
process that took place in
solving this equation
*Students will answer
this on their paper

Discuss the Composition of Functions,
illustration and its examples.
*Students will answer
the questions regarding
the steps in solving
problem.
*AssignmentStudent will answer this
on their paper.
Assignment
Evaluate the given composite
functions.
 𝒇(𝒙) = −𝟑𝒙 + 𝟕 and
𝒈(𝒙) = 𝟐𝒙𝟐 − 𝟖
Given the following functions f and g
above, find and simplify the following
functions
1.
𝒇(𝒈(𝒙))
2.
(𝒈 ∘ 𝒇)(𝒙)
3.
If 𝒇(𝒙) = −𝟗𝒙 − 𝟗 and
𝒈(𝒙) = √𝒙 − 𝟗
Find (𝒇 ∘ 𝒈)(𝟏𝟎)
Prepared by:
Checked by:
Ms. Mary Grace S. Villarosa
SHS – Faculty
Rosahle S. Pagadora, MS
SHS - Principal